# A Challenging Problem of Decahedron With 10 Congruent Right Kite Faces

Geometry Level 5

The diagram above shows a decahedron that has 10 congruent faces each as a right kite (i.e. a cyclic quadrilateral consisting of two congruent right triangles with common hypotenuse).

It has two pairs of unequal sides $$a,b$$ with $$a<b$$.

And also has 12 vertices which exactly lie on a spherical surface with certain radius $$R$$.

If $$b=15$$, then what is the value of radius $$R$$?

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